Question E.3: Use MATLAB to solve for the mesh currents in the circuit in ......
Use MATLAB to solve for the mesh currents in the circuit in Fig. E.6.
For the four meshes,
– 6 + 9I_{1} – 4 I_{2} – 2 I_{4} = 0 → 6 = 9 I_{1} – 4 I_{2} – 2 I_{4} (E.3.1)
12 + 15 I_{2} – 4 I_{1} – 4 I_{3} – 6 I_{4} = 0 →
– 12 = – 4 I_{1} + 15 I_{2} – 4 I_{3} – 6 I_{4} (E.3.2)
– 12 + 10 I_{3} – 4 I_{2} – 2 I_{4} = 0 → 12 = – 4 I_{2} + 10 I_{3} – 2 I_{4} (E.3.3 )
20 I_{4} – 2 I_{1} – 6 I_{2} – 2 I_{3} = 0 → 0 = – 2 I_{1} – 6 I_{2} – 2 I_{3} + 20 I_{4} (E.3.4)
Putting Eqs. (E.3.1) to (E.3.4) together in matrix form, we have
\begin{bmatrix} 9 & -4 & 0 & -2 \\ -4 & 15 & -4 & -6 \\ 0 & -4 & 10 & -2 \\ -2 & -6 & -2 & 20 \end{bmatrix} \begin{bmatrix} I_{1}\\I_{2} \\ I_{3}\\ I_{4} \end{bmatrix} = \begin{bmatrix} 6 \\ -12 \\ 12 \\ 0 \end{bmatrix}
or AI = B , where the vector I contains the unknown mesh currents.
Script File
We now use MATLAB to determine I as follows:
>> A = [9 -4 0 -2 ; -4 15 -4 -6;
0 -4 10 -2 ; -2 -6 -2 20]
A =
9 -4 0 -2
-4 15 -4 -6
0 -4 10 -2
-2 -6 -2 20
>> B = [6 -12 12 0]’
B =
6
-12
12
0
>> I = inv(A)*B
I =
0.5203
-0.3555
1.0682
0.0522
Thus, I_{1} = 0.5203 , I_{2} = - 0.3555 , I_{3} = 1.0682 , I_{4} = 0.0522 A .